Question
Find three mutually orthogonal unit vectors in $\mathbb{R}^{3}$ besides $\pm \mathbf{i}, \pm \mathbf{j}$ and $\pm \mathbf{k}$.
Step 1
This is a unit vector because its length is $\sqrt{1^2 + 1^2 + 0^2} = \sqrt{2}$, so we normalize it to get $\mathbf{u}_1 = \frac{1}{\sqrt{2}}(1,1,0)$. Show more…
Show all steps
Your feedback will help us improve your experience
Linh Vu and 74 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let $a$ and $b$ be real numbers. Find three mutually orthogonal unit vectors in $\mathbb{R}^{3}$ besides $\pm \mathbf{i}, \pm \mathbf{j}$ and $\pm \mathbf{k}$
Vectors and Vector-Valued Functions
Dot Products
Find two unit vectors orthogonal to both $\mathbf{j}-\mathbf{k}$ and $\mathbf{i}+\mathbf{j}$.
VECTORS AND THE GEOMETRY OF SPACE
The Cross Product
Find two unit vectors orthogonal to both $\mathbf{i}+\mathbf{j}+\mathbf{k}$ and $2 \mathbf{i}+\mathbf{k} .$
Vectors and the Geometry of Space
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD
